To Both Ed and Al.
Thanks!
I guessed it was a gradual change subject to
length and shape of the inlet duct/ diffuser.
I had hoped that with a decent design (we
are all aiming for) that you might expect to achieve max static pressure
well prior to the Radiator.
However it may be that the optimum static
pressure might be design dependent and happen just before the rad. If
figure if it was within the rad it would be restrictive.
Thinking on it further, the more further
forward (of the Rad face) the optimum static air pressure is, it may
suggest that the rad is too restrictive.
I'm not sorry I asked, a little less
confused and more things to think about.
George ( down under)
George, here you are getting into something we have
not discussed in depth.
Two equations/laws of fluid dynamics are
involved. Bernoulli's equation and an equation called the law of
continuity. This equation relates to the fact that you
don't create or lose mass in the duct, so the mass flow is a constant
everywhere in the duct. The mass flow is frequently shown as the
product of air density*cross section area*air velocity = mass flow or
simply p*A*V
The equation goes something like this, the
p1A1V1 (mass flow at point 1) =
p2A2V2 (mass flow at point 2). Since the air is
normally considered to act like it is incompressible at the lower speeds
we are talking about, that means the density p1=
p2, so we can drop them from the equation for this
explanation.
That leaves us with A1V1 = A2V2 or
the product of the area and velocity at point 1 is equal to the area and
velocity at point 2 in the duct. Now if A1 = A2
then V1 has to equal V2 for the two
sides of the equation to be equal. But, what if
A2 = 2* A1 or the cross section area of point 2 is
made twice the cross section area of point 1. Then if
A2 = 2*A1, we can substitute 2*A1 for
A2 in the equation and we have the
following.
Taking A1V1 = A2V2 and substituting
we have A1*V1 = (2*A1)*V2. So what does that
tell us about the air velocity at point 2 now that we have doubled the
cross section area there?
Well solving the equation for the new V2, We can
call the new velocity at point 2 V2n
(for V2 new) with V2o being the old velocity at point
2.
So we have V2n
= A1V2o/(2*A1) Now we can cancelled the
A1 in the numerator and denominator on right side
of the equation leaving
V2n =
V2o/2 This shows us that the
new velocity at point 2, V2n is 1/2 the old velocity
(V2o) at point 2 or V2n =
0.5V2o
So what this says is the velocity
starts changing (slowing in this case and the pressure
increasing ) as soon as the cross section area A2 starts
to increase from A1. The process continues until the area stops
expanding (or the kinetic energy of the moving air has all been converted
to a static pressure increase) and that is where the process is
finished as the duct/diffuser has expanded to its maximum area.
Actually, this process happens with both nozzles and diffusers just the
opposite way. Its derived from the Bernoulli equation and the
continuity law.
So if you had a duct whose cross section area
continued to expand for a distance of 2" or 20" or 200" then
theoretically the pressure would continue to build and the velocity to
decrease until all of the kinetic energy of the moving air has been
converted to pressure increase. This is all theoretical, there are
losses and turbulence and etc, that makes a difference, but you get the
ideal. It depends on your specific diffuser dimensions.
Think of it this way, George, some wind tunnels have
diffuser which expand over 10's of feet while some microscopic cooling
systems have diffusers measured in 10th's of an inch.
Now aren't you sorry you asked
{:>)?
Ed
----- Original Message -----
Sent: Friday, November 09, 2007
4:52 PM
Subject: [FlyRotary] Re:
Total,duct, Ambient or Velocity????
Ed and Al,
This is all good info me, it either
confirms, clarifies or informs.
The straw concept is a timely reminder of
pressure differentials, a good example IMHO.
One thing I would really love to know is -
at what point in the inlet duct does the dynamic flow change to static
pressure. I would assume this would vary with different shaped ducts and
different dynamic flow ( airflow speed).
Your opinions on this or guesstimates
ie 1", 2" or 3" from the face of the rad, would be of great
interest to me.
George (down under)
Hi Al,
Not picky - some good points as always .
Yes, I agree, generalization does have its pit falls,
but on the other hand I think they can help promote a conceptual
understanding which can be refined (through study and experiments) to
meet a particular situation. As we know, cooling airflow is
attempting to balance conflicting aerodynamic and thermodynamic
principles.
I also agree that much of this stuff
addresses the "Perfect theoretical duct" out of necessity as there is
only one perfect duct but many, many implementations
that fall short of perfect. So its more of a
conceptual goal to be aimed for - it may never be achieved,
but provides at least guidelines. But,this is
just my opinion of course.
Actually, I disagree, you can not "suck" air
though anything. You may create a partial pressure difference
with the fan, but it is the higher pressure air on the other end of
the duct that pushes or "blows" air through the duct into the area of
lower pressure {:>) .
But, semantics aside, yes, I agree, lower
exit pressure is what you are after and that does not always equate to
larger exit duct area. In fact, if the air heated by the core
flows through a nozzle it might even produce thrust and lower exit
pressure using a smaller exit. But, in general, I still
believe that in most of our cases, we are short of the level of duct
design that would reliably permit that. What we need is someone
to invest in one of those $$$$ Computer Fluid Flow software programs
and see what they would reveal.
Ed
----- Original Message -----
Sent: Friday, November 09, 2007
1:09 AM
Subject: [FlyRotary] Re:
Total,duct, Ambient or Velocity????
It
would seem "reasonable" that a low pressure area at the exit
will help flow through a duct - no argument on that
point. What the report appeared to say is that the after a
certain point opening the exit area wider does not appear to have
any additional benefit. (Exit “area” and exit “pressure” are not
interchangeable terms) That if the duct is capable of
"using up" all of the kinetic energy in your air flow by
obstructions, pressure drops and friction losses then
enlarging the exit does not necessarily add to the
flow.
Remember
you can not suck air through a duct, you can only blow it
through. (Of course
you can suck air through a duct – I do it after (and sometimes
before) every flight with the fan I have on the back side of the
radiator) So in effect if the straw is pinched you can
"suck" on it all you want but it won't increase flow
{:>).
If I
understood the report, it appears that enlarging the exit area
beyond the frontal area of your core provides little if any
additional benefit. That does not mean cowl flaps never work
or provide benefit. In fact it appears that the better your
duct, the more benefit the cowl flaps appear to have, the
worst your duct, the lesser benefit - just the opposite of what you
might think.
Ed;
Don’t
mean to be picky, but some of these generalities are making me
nervousJ.
These things are applicable only when the duct/diffuser is operating
at max efficiency – which is rarely the case.
Lot’s of
good info.
Thanks. You’re right; it’s some kind of magic, and you don’t
know for sure until you built it and try it.
Al
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